A023114 Squares that remain square when the digit 9 is appended.

0, 4, 16, 324, 6400, 23716, 467856, 9229444, 34199104, 674648676, 13308852496, 49315084900, 972842923584, 19191356070436, 71112318227344, 1402838821160100, 27673922144716864, 102543913568745796, 2022892607269941264

Offset

1,2

Comments

The terms of the sequence are the squares of the y-values in the solution to the Pellian equation x^2-10*y^2=9. - Colin Barker, Sep 28 2013

Links

Table of n, a(n) for n=1..19.

Formula

Empirical g.f.: -4*x^2*(x+1)*(x^4+2*x^3+75*x^2+2*x+1) / ((x-1)*(x^6-1442*x^3+1)). - Colin Barker, Jan 31 2013

Mathematica

Select[Range[0, 10^6]^2, IntegerQ[Sqrt[10#+9]]&] (* The program generates the first 13 terms of the sequence. *) (* Harvey P. Dale, Jul 21 2024 *)

Crossrefs

Cf. A023111, A023112, A023113.

Sequence in context: A273474 A095956 A014731 * A207851 A202681 A067211

Adjacent sequences: A023111 A023112 A023113 * A023115 A023116 A023117

Keyword

nonn,base

Author

David W. Wilson

Status

approved